Dominance for enclosure problems

Waseem Akram () and Sanjeev Saxena ()
Additional contact information
Waseem Akram: Indian Institute of Technology
Sanjeev Saxena: Indian Institute of Technology

Journal of Combinatorial Optimization, 2025, vol. 50, issue 4, No 10, 20 pages

Abstract: Abstract Two triangles in the plane are called homothetic if one can be obtained from the other using scaling and translation operations. In this paper, we investigate an enclosure problem involving homothetic triangles. Specifically, the problem is to preprocess a given set of n homothetic triangles so that the triangles enclosing (or containing) a query object can be found quickly. The query objects we consider include points, line segments, trapezoids, and ellipses. We propose an efficient solution to the problem using the 3-D dominance searching. Our results can also be extended to higher dimensions. Moreover, we also present a negative result that suggests that the enclosure problem involving (arbitrarily) axis-parallel right-angled triangles may not be solvable using 4-D dominance searching.

Keywords: Geometric intersection; Dominance; Algorithms; Data structures (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-025-01373-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:50:y:2025:i:4:d:10.1007_s10878-025-01373-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-025-01373-5

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().